The second allegation centres on a claim that Mr Netanyahu received gifts worth at least a million shekels ($283,000; £204,000) from Hollywood mogul Arnon Milchan and other supporters.

The Jerusalem Post says the gifts included champagne and cigars, and were given in exchange for help getting Mr Milchan a US visa.

Mr Milchan, the producer of films including Fight Club, Gone Girl and The Revenant, should face bribery charges, police said.

The police statement said that Mr Netanyahu, after receiving gifts, pushed for the Milchan Law, which would have ensured that Israelis who return to live in Israel from abroad were exempt from paying taxes for 10 years.

Police say Mr Netanyahu is also suspected of fraud and breach of trust in a case involving Australian billionaire James Packer.

Israel's Channel 10 reported in December that Mr Packer told investigators he gave the prime minister and his wife Sara gifts.

A spokesman for Mr Packer told Reuters "there is no allegation of wrongdoing" on the part of his client, and both Israeli and Australian police had "confirmed he was interviewed as a witness, not a suspect".